1. Field
This invention relates to methods of delaying light using leaky-mode resonant elements. The methods and devices disclosed can be applied, for example, in dispersion management and engineering in telecommunication systems, in laser systems, in optical logic devices, and in nanoelectronic and nanophotonic chips.
2. Description of the Related Art
Materials that are artificially structured on a nanoscale exhibit electronic and photonic properties that differ dramatically from those of the corresponding bulk entity. In particular, subwavelength photonic lattices are of immense interest owing to their applicability in numerous optical systems and devices including communications, medicine, and laser technology [J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton, 1995); A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th edition (Oxford University Press, New York, 2007); K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001)]. When the lattice is confined to a layer, thereby forming a periodic waveguide, an incident optical wave may undergo a guided-mode resonance (GMR) on coupling to a leaky eigenmode of the layer system. The external spectral signatures can have complex shapes with high efficiency in both reflection and transmission [P. Vincent and M. Neviere, “Corrugated dielectric waveguides: A numerical study of the second-order stop bands,” Appl. Phys. 20, 345-351 (1979); L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Comm. 55, 377-380 (1985); E. Popov, L. Mashev, and D. Maystre, “Theoretical study of anomalies of coated dielectric gratings,” Opt. Acta 33, 607-619 (1986); G. A. Golubenko, A. S. Svakhin, V. A. Sychugov, and A. V. Tishchenko, “Total reflection of light from a corrugated surface of a dielectric waveguide,” Soy. J. Quantum Electron. 15, 886-887 (1985); I. A. Avrutsky and V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36, 1527-1539 (1989); R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022-1024 (1992); S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606-2613 (1993)].
It has been shown that subwavelength periodic leaky-mode waveguide films with one-dimensional periodicity provide diverse spectral characteristics such that even single-layer elements can function as narrow-line bandpass filters, polarized wideband reflectors, wideband polarizers, polarization-independent elements, and wideband antireflection films [Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12, 5661-5674 (2004); Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to fashion diverse optical spectra,” Opt. Express, 12, 1885-1891 (2004)]. The spectra can be further engineered with additional layers [M. Shokooh-Saremi and R. Magnusson, “Wideband leaky-mode resonance reflectors: Influence of grating profile and sublayers,” Opt. Express 16, 18249-18263 (2008)]. The relevant physical properties of these elements can be explained in terms of the structure of the second (leaky) photonic stopband and its relation to the symmetry of the periodic profile. The interaction dynamics of the leaky modes at resonance contribute to sculpting the spectral bands. The leaky-mode spectral placement, their spectral density, and their levels of interaction strongly affect device operation and functionality [Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12, 5661-5674 (2004)]. There has been a considerable amount of research performed on the spectral attributes of these elements with many useful applications proposed. In contrast, little has been done to understand their dispersive properties and related slow-light applications.
Optical delay lines have important roles in communication systems and in radio-frequency (RF) photonics. They are common in optical time-division multiplexed communication systems for synchronization and buffering and in RF phased arrays for beam steering [G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37, 525-532 (2001)]. These delay lines are implemented, for example, as free-space links, fiber-based links, fiber-Bragg gratings, and ring resonators. The delay properties are based on the phase response of the medium or filter in which the delay line is implemented as discussed in detail by Lenz et al. in [G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37, 525-532 (2001)]. Many examples of practical delay systems are reported in [C. K. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photonics Technol. Lett. 10, 994-996 (1998); G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control,” J. Lightwave Technol. 17, 1248-1254 (1999); C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Cappuzzo, L. T. Gomez, and R. E. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photonics Technol. Lett. 11, 1623-1625 (1999); M. S. Rasras, C. K. Madsen, M. A. Cappuzzo, E. Chen, L. T. Gomez, E. J. Laskowski, A. Griffin, A. Wong-Foy, A. Gasparyan, A. Kasper, J. Le Grange, and S. S. Patel, “Integrated resonance-enhanced variable optical delay lines,” IEEE Photonics Technol. Lett. 17, 834-836 (2005)] using all-pass optical filters.
Advances in nanofabrication and nanolithography are placing the long-awaited photonic integrated circuit in view as an attainable goal. The all-optical networks of the future will bypass optical-to-electrical converters, thereby eliminating associated noise and considerably reducing the attendant bit error rates. As discussed by Parra and Lowell, all-optical processing requires slow-light-enabled synchronizers, buffers, switches, and multiplexers [E. Parra and J. R. Lowell, “Toward applications of slow light technology,” Opt. Photon. News, 40-45 (November 2007)]. The technology needed to generate these functions for mass deployment is not available today, but there is a considerable amount of research being devoted to develop it. Means to realize these valuable slow-light applications include stimulated (Brillouin, Raman) scattering in fibers, semiconductor optical amplifiers, 2D photonic crystals, atomic vapors, and high-finesse ring resonators [E. Parra and J. R. Lowell, “Toward applications of slow light technology,” Opt. Photon. News, 40-45 (November 2007)].
Previous small-footprint devices include devices such as 2D photonic-crystal (PhC)-based micro-resonator chips [M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nature Photon. 2, 741-747 (2008); F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nature Photon. 1, 65-71 (2006)]. These coupled-resonator optical waveguides (CROW) may contain hundreds of high-Q cavities within a PhC lattice. These cavities, formed by slightly offset lattice holes, are perhaps ˜2000 nm in diameter. Experimentally, CROW structures can attain group velocity below 0.01 c and long group delays as shown by Notomi et al. [M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nature Photon. 2, 741-747 (2008)].
The amplitude-based spectral response of leaky-mode elements has been extensively investigated. Although the phase response of these elements has received less attention, there has been some investigation in this area. For example, Schreier et al. treated a sinusoidally modulated waveguide grating at oblique incidence, computing the phase variation of the reflectance near resonance relative to modulation strength [F. Schreier, M. Schmitz, and 0. Bryngdahl, “Pulse delay at diffractive structures under resonance conditions,” Opt. Lett. 23, 1337-1339 (1998)]. They quantified the degree to which the structural parameters control the amount of delay achievable with computed values of delay ranging from sub-ps to ˜40 ps depending on conditions. Using a finite-difference time-domain computational approach, Mirotznik et al. evaluated the temporal response of a subwavelength dielectric grating that we designed previously as a reflection-type GMR element [M. S. Mirotznik, D. W. Prather, J. N. Mait, W. A. Beck, S. Shi, and X. Gao, “Three-dimensional analysis of subwavelength diffractive optical elements with the finite-difference time-domain method,” Appl. Opt. 39, 2878-2879, (2000); S. Tibuleac and R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14, 1617-1626 (1997)]. The model input pulse was Gaussian with center wavelength of 510 nm, spectral width of 5000 nm, and temporal pulse width of ˜5 fs. They noted that the reflected energy persisted for ˜1 ps after the incident field decayed. Later, Suh et al. designed a 2D photonic-crystal-slab-type GMR transmission filter computing the resonance amplitude, transmission spectrum, and group delay. For a 1.2 μm thick slab, a peak delay of about 10 ps was obtained at 1550 nm; the spectral width of the response was ˜0.8 nm [W. Suh and S. Fan, “All-pass transmission or flattop reflection filters using a single photonic crystal slab,” Appl. Phys. Lett. 84, 4905-4907 (2004)]. Nakagawa et al. presented a method to model ultra-short optical pulse propagation in periodic structures, based on the combination of Fourier spectrum decomposition and rigorous coupled-wave analysis (RCWA) [W. Nakagawa, R. Tyan, P. Sun, F. Xu, and Y. Fainman, “Ultrashort pulse propagation in near-field periodic diffractive structures by use of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A 18, 1072-1081 (2001)]. They simulated an incident pulse (167 fs) on a resonant grating supporting two modes and found that two pulses were transmitted with shape similar to the excitation pulse shape. Vallius et al. modeled spatial and temporal pulse deformations generated by GMR filters. They illuminated the structure with a Gaussian temporal pulse of 2 ps duration and 633 nm wavelength. Lateral spread and temporal decompression were observed in the reflected and transmitted pulses [T. Vallius, P. Vahimaa, and J. Turunen, “Pulse deformations at guided-mode resonance filters,” Opt. Express 10, 840-843, (2002)]. As the spectrum of the pulse was not well accommodated by the GMR element, the reflection efficiency of the pulse was relatively low.